The article is arranged as follows. Sec. presents a brief introduction to \(f(R)\)  gravity and the cosmological field equations field equations for \(f(R)\)  gravity. Sec. presents the earliest and the very basic dynamical system formulation for \(f(R)\)  gravity [1]}, [2]}, [3]}. Sec. reviews the usual and most used dynamical system formulation in terms of expansion-normalized dynamical variables [4]}, [5]} and points out it's shortcoming. Sec. describes the alternative dynamical system formulation as was proposed by Carloni [6]}. Sec. presents the form-independent dynamical system formulation as proposed by Chakraborty et al. [7]}. Sec.  briefly introduces the compact dynamical system formulation and presents some of its strengths and flaws. Finally a discussion is presented in Sec..
